Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9002	2^203642+39	61303	Lelio R Paula	08/2011
9001	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012
9003	11^58849-6040	61285	Enzo Doria	02/2013
9004	43694!3-3	61264	Robert Price	10/2014
9005	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
9006	2^203490+12909	61257	Lelio R Paula	10/2011
9007	(16*10^61251-31)/3	61252	Robert Price	03/2016
9008	20^47077-5703	61249	Enzo Doria	03/2013
9009	2^203434-113081	61240	Enzo Doria	07/2014
9011	5^87606+4	61234	Wojciech Florek	11/2005
9010	2^203412-167	61234	Lelio R Paula	08/2011
9012	2^203402+1089	61231	Lelio R Paula	10/2011
9013	(8*10^61230+67)/3	61231	Robert Price	01/2017
9014	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
9015	1265^19732+19732^1265	61211	Serge Batalov	05/2014
9016	2^203330+145	61209	Lelio R Paula	08/2011
9017	6^78647-137	61200	Lelio R Paula	04/2013
9018	85^31718+84	61198	Norbert Schneider	10/2015
9019	11^58763-270	61196	Enzo Doria	07/2012
9020	2^203285-112321	61195	Enzo Doria	06/2014
9021	2^203253-995143	61186	Paul Bourdelais	11/2012
9022	15319^9862+9862^15319	61184	Hans Havermann	07/2016
9023	7^72395-44	61181	Lelio R Paula	04/2013
9024	(49*10^61167-67)/9	61168	Robert Price	08/2017
9025	5*2^203176-7	61163	Lelio R Paula	04/2014
9026	(26*10^61156-413)/9	61157	Robert Price	10/2017
9028	7^72358+54	61150	Lelio R Paula	04/2013
9027	2^203133-111775	61150	Enzo Doria	05/2014
9029	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
9030	2^203112-18009	61143	Enzo Doria	05/2013
9031	43607!3+729	61129	Robert Price	09/2014
9032	2^203065-114853	61129	Enzo Doria	05/2015
9033	3^128111+196	61125	Lelio R Paula	04/2013
9034	128^29007+29007^128	61124	Serge Batalov	05/2014
9035	4*10^61119+49	61120	Robert Price	08/2017
9036	22355*2^203009-3	61117	Donovan Johnson	03/2004
9037	2^203018+33	61115	Lelio R Paula	08/2011
9038	2^203017-1615	61115	Lelio R Paula	10/2011
9039	16697^4570+4570^16697	61110	Hans Havermann	12/2016
9040	2^202998-17241	61109	Enzo Doria	05/2013
9041	20^46964+93	61102	Lelio R Paula	06/2013
9042	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
9043	20^46960-5463	61097	Enzo Doria	03/2013
9044	(11*10^61095+49)/3	61096	Robert Price	05/2016
9045	14040^14731-14731^14040	61095	Norbert Schneider	04/2019
9046	2^202934-5955	61090	Lelio R Paula	10/2011
9047	19^47772-68	61089	Lelio R Paula	05/2013
9048	2^202877-499423	61073	Paul Bourdelais	03/2013
9049	2^202763-17125	61038	Enzo Doria	05/2013
9050	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
9051	14788^13355+13355^14788	61011	Hans Havermann	12/2016
9052	16069^6258+6258^16069	61005	Hans Havermann	12/2016
9053	5^87276-14336	61004	Enzo Doria	02/2013
9054	50^35899-49^35899	60992	Robert Price	12/2012
9055	10^60991+123456789	60992	Robert Price	10/2019
9056	2^202599-3049	60989	Yves Minet	10/2014
9057	2^202535-111571	60970	Enzo Doria	05/2014
9058	(13*10^60966+107)/3	60967	Robert Price	11/2017
9060	10^60959+57	60960	Patrick De Geest	12/2008
9059	6*10^60959-91	60960	Robert Price	11/2017
9062	10^60959-60959	60959	Henri Lifchitz	08/2002
9061	10^60959-29177	60959	Patrick De Geest	08/2008
9063	5^87206+4^(87206+1)	60955	Robert Price	07/2016
9064	2^202476-15909	60952	Enzo Doria	04/2013
9065	2^202472-17513	60951	Enzo Doria	05/2013
9066	14858^12651+12651^14858	60950	Hans Havermann	12/2016
9067	2^202389-58695	60926	Lelio R Paula	09/2011
9068	3^127597-34	60880	Lelio R Paula	04/2013
9069	15088^10831+10831^15088	60876	Hans Havermann	12/2016
9070	2^202198-113261	60868	Enzo Doria	07/2014
9071	2^202182+135	60863	Lelio R Paula	08/2011
9072	2^202176+85	60862	Lelio R Paula	08/2011
9073	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
9074	(31*2^202163+1)/3	60859	Lelio R Paula	03/2012
9075	14708^13707+13707^14708	60847	Hans Havermann	12/2016
9076	2^202112+202112^2-1	60842	Robert Price	04/2014
9077	(13*2^202142-1)/405984274257	60841	Lelio R Paula	01/2014
9078	64743*10^60832+(6^78175-11)/5	60837	Gilbert Mozzo	05/2012
9079	(19*2^202098-1)/6795	60836	Lelio R Paula	01/2014
9080	(6^78175-11)/5	60832	Paul Bourdelais	11/2011
9081	2^202063+1605	60828	Lelio R Paula	09/2011
9082	2^202058+859	60826	Lelio R Paula	09/2011
9083	1576^19021+19021^1576	60821	Serge Batalov	05/2014
9084	(2^202009+3)/6005	60807	Lelio R Paula	03/2012
9085	10^60776+3	60777	Robert Price	01/2011
9086	10^60776-14819	60776	Patrick De Geest	12/2012
9087	55*10^60772+7	60774	Robert Price	10/2017
9088	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
9089	14801^12750+12750^14801	60766	Hans Havermann	05/2019
9090	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
9091	2^201822-177	60755	Lelio R Paula	08/2011
9092	(13*10^60744+17)/3	60745	Robert Price	06/2015
9093	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
9094	(26*10^60717-71)/9	60718	Robert Price	03/2015
9095	37^38712-2	60709	Lelio R Paula	08/2013
9096	2^201657-112003	60705	Enzo Doria	05/2014
9097	(10^60703+3^60703)/13	60702	Robert Price	01/2013
9098	2^201622-112817	60695	Enzo Doria	06/2014
9099	2^201620-17177	60694	Enzo Doria	05/2013
9100	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
9101	2^201609-49789	60691	Henri Lifchitz	03/2005
9102	2^201582-19061	60683	Enzo Doria	05/2013
9103	43316!3+27	60679	Robert Price	09/2014
9104	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
9105	2^201560+105	60676	Lelio R Paula	08/2011
9106	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
9107	2^201545-18021	60672	Enzo Doria	05/2013
9108	2^201543+11715	60671	Lelio R Paula	09/2011
9109	2^201512-111755	60662	Enzo Doria	05/2014
9110	p(13013)#/2+64	60662	Robert Price	03/2017
9111	15962^6315+6315^15962	60662	Hans Havermann	05/2019
9112	11^58248+16	60660	Lelio R Paula	05/2013
9113	2^201496-27	60657	Lelio R Paula	08/2011
9114	5*10^60655+57	60656	Robert Price	11/2017
9115	16239^5432+5432^16239	60653	Hans Havermann	05/2019
9116	(7*10^60643+197)/3	60644	Robert Price	07/2017
9117	2^201426-16097	60636	Enzo Doria	04/2013
9118	(17*10^60631-11)/3	60632	Robert Price	07/2015
9119	6^77916-77	60631	Lelio R Paula	04/2013
9120	(27*2^201410-1)/491	60630	Lelio R Paula	01/2014
9121	5^86727+98	60620	Lelio R Paula	04/2013
9122	17^49266-26	60620	Lelio R Paula	05/2013
9123	20^46589-33	60614	Lelio R Paula	05/2013
9124	11825^14882-14882^11825	60612	Norbert Schneider	08/2019
9126	6^77889+65	60610	Lelio R Paula	04/2013
9125	14921^11536+11536^14921	60610	Hans Havermann	05/2019
9127	139901#+148387	60595	Nicolas PALAU	09/2016
9128	2^201285-111723	60593	Enzo Doria	05/2014
9129	46199*2^201268+129647	60593	Paul Vanderveen	11/2016
9131	3^126991-100	60591	Lelio R Paula	04/2013
9130	2^201278-111623	60591	Enzo Doria	05/2014
9132	5^86682-16004	60589	Enzo Doria	05/2014
9133	(865*10^60583-1)/9	60585	Robert Price	11/2017
9134	(58*10^60579+221)/9	60580	Robert Price	02/2017
9135	9*2^201231-5	60578	Lelio R Paula	04/2014
9136	4*10^60572-89	60573	Robert Price	08/2017
9137	(78557*2^201207+1)/13067	60571	Lelio R Paula	06/2014
9138	2^201186-66945	60564	Lelio R Paula	09/2011
9139	2^201186-94395	60564	Lelio R Paula	09/2011
9140	65^33403+32	60557	Lelio R Paula	01/2016
9141	103^30079+102	60545	Norbert Schneider	10/2016
9142	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
9143	2^201098-17717	60537	Enzo Doria	05/2013
9144	(3^126881+8)/4829	60534	Lelio R Paula	03/2012
9145	2^201074+75049	60530	Enzo Doria	04/2016
9146	11^58111-1290	60517	Enzo Doria	11/2012
9147	(509203*2^201012-1)/9	60516	Lelio R Paula	04/2015
9148	(2^200997+103590)/2	60506	Stefano Morozzi	10/2019
9149	(2^200995+12966)/2	60506	Stefano Morozzi	10/2019
9150	(2^200996+41746)/2	60506	Stefano Morozzi	10/2019
9151	(2^200994+88474)/2	60505	Stefano Morozzi	10/2019
9152	(2^200988+69570)/2	60504	Stefano Morozzi	10/2019
9153	(2^200989+91374)/2	60504	Stefano Morozzi	10/2019
9154	(2^200988+1162)/2	60504	Stefano Morozzi	10/2019
9155	(2^200986+141282)/2	60503	Stefano Morozzi	10/2019
9156	(2^200987+98834)/2	60503	Stefano Morozzi	10/2019
9157	(2^200987+134150)/2	60503	Stefano Morozzi	10/2019
9158	(2^200987+36306)/2	60503	Stefano Morozzi	10/2019
9159	(2^200978+102474)/2	60501	Stefano Morozzi	10/2019
9160	(2^200978+193794)/2	60501	Stefano Morozzi	10/2019
9161	(2^200979+102630)/2	60501	Stefano Morozzi	10/2019
9162	(2^200979+197418)/2	60501	Stefano Morozzi	10/2019
9163	(2^200979+20934)/2	60501	Stefano Morozzi	10/2019
9164	(2^200979+57186)/2	60501	Stefano Morozzi	10/2019
9165	(2^200980+1590)/2	60501	Stefano Morozzi	10/2019
9166	(2^200980+59802)/2	60501	Stefano Morozzi	10/2019
9169	14447^14544-14544^14447	60500	Norbert Schneider	12/2018
9167	(2^200976+64590)/2	60500	Stefano Morozzi	10/2019
9168	(2^200975+59534)/2	60500	Stefano Morozzi	10/2019
9170	(2^200974+73402)/2	60499	Stefano Morozzi	10/2019
9171	(2^200974+108894)/2	60499	Stefano Morozzi	10/2019
9172	(2^200970+184858)/2	60498	Stefano Morozzi	10/2019
9173	(2^200968+60306)/2	60498	Stefano Morozzi	10/2019
9174	(2^200966+152370)/2	60497	Stefano Morozzi	10/2019
9175	(2^200967+124070)/2	60497	Stefano Morozzi	10/2019
9176	(2^200962+131130)/2	60496	Stefano Morozzi	10/2019
9177	(2^200963+178446)/2	60496	Stefano Morozzi	10/2019
9178	(2^200964+74382)/2	60496	Stefano Morozzi	10/2019
9179	(2^200964+43006)/2	60496	Stefano Morozzi	10/2019
9180	(2^200958+75810)/2	60495	Stefano Morozzi	10/2019
9181	(2^200960+78558)/2	60495	Stefano Morozzi	10/2019
9182	(2^200960+172818)/2	60495	Stefano Morozzi	10/2019
9183	(2^200957+141246)/2	60494	Stefano Morozzi	10/2019
9184	(2^200957+22682)/2	60494	Stefano Morozzi	10/2019
9185	(2^200948+86266)/2	60492	Stefano Morozzi	10/2019
9186	(2^200951+117594)/2	60492	Stefano Morozzi	10/2019
9187	(2^200946+75378)/2	60491	Stefano Morozzi	10/2019
9188	(2^200945+4386)/2	60491	Stefano Morozzi	10/2019
9189	(2^200943+133266)/2	60490	Stefano Morozzi	10/2019
9190	(2^200944+81006)/2	60490	Stefano Morozzi	10/2019
9191	(2^200944+142678)/2	60490	Stefano Morozzi	10/2019
9192	(2^200944+171490)/2	60490	Stefano Morozzi	10/2019
9193	(2^200944+9898)/2	60490	Stefano Morozzi	10/2019
9194	(2^200939+96774)/2	60489	Stefano Morozzi	10/2019
9195	(2^200938+28914)/2	60489	Stefano Morozzi	10/2019
9196	(2^200940+62406)/2	60489	Stefano Morozzi	10/2019
9197	(2^200935+177198)/2	60488	Stefano Morozzi	10/2019
9198	(2^200934+92118)/2	60487	Stefano Morozzi	10/2019
9199	(2^200934+118038)/2	60487	Stefano Morozzi	10/2019
9200	(2^200934+136914)/2	60487	Stefano Morozzi	10/2019
9201	(2^200929+119030)/2	60486	Stefano Morozzi	10/2019
9202	(2^200928+25398)/2	60486	Stefano Morozzi	10/2019
9203	(2^200925+112382)/2	60485	Stefano Morozzi	10/2019
9204	(2^200926+37230)/2	60485	Stefano Morozzi	10/2019
9205	(2^200922+145038)/2	60484	Stefano Morozzi	10/2019
9206	(2^200922+158602)/2	60484	Stefano Morozzi	10/2019
9207	(2^200923+123050)/2	60484	Stefano Morozzi	10/2019
9208	(2^200918+124762)/2	60483	Stefano Morozzi	10/2019
9209	(2^200919+75986)/2	60483	Stefano Morozzi	10/2019
9210	(2^200919+188430)/2	60483	Stefano Morozzi	10/2019
9211	(2^200920+80118)/2	60483	Stefano Morozzi	10/2019
9212	(2^200921+86102)/2	60483	Stefano Morozzi	10/2019
9213	(2^200918+34962)/2	60483	Stefano Morozzi	10/2019
9214	(2^200919+62018)/2	60483	Stefano Morozzi	10/2019
9215	(2^200920+610)/2	60483	Stefano Morozzi	10/2019
9216	(2^200915+3990)/2	60482	Stefano Morozzi	10/2019
9218	2^200911+5711	60481	Lelio R Paula	10/2011
9217	(2^200912+124510)/2	60481	Stefano Morozzi	10/2019
9219	(2^200912-3)/23	60480	Lelio R Paula	03/2012
9220	(2^200910+184662)/2	60480	Stefano Morozzi	10/2019
9221	(2^200911+193034)/2	60480	Stefano Morozzi	10/2019
9222	(2^200908+62142)/2	60480	Stefano Morozzi	10/2019
9223	(2^200907+135174)/2	60479	Stefano Morozzi	10/2019
9225	18^48179-17^48179	60478	Jean-Louis Charton	12/2010
9224	(2^200904+6270)/2	60478	Stefano Morozzi	10/2019
9226	(2^200898+192858)/2	60477	Stefano Morozzi	10/2019
9227	(2^200899+30038)/2	60477	Stefano Morozzi	10/2019
9231	38^38281-37^38281	60476	Robert Price	09/2012
9230	4*7^71560-3	60476	Lelio R Paula	09/2014
9228	(2^200895+175746)/2	60476	Stefano Morozzi	10/2019
9229	(2^200896+151750)/2	60476	Stefano Morozzi	10/2019
9232	(2^200892+64762)/2	60475	Stefano Morozzi	10/2019
9233	(2^200891+176474)/2	60474	Stefano Morozzi	10/2019
9234	(2^200885+133886)/2	60473	Stefano Morozzi	10/2019
9235	(2^200886+77362)/2	60473	Stefano Morozzi	10/2019
9236	(2^200879+149450)/2	60471	Stefano Morozzi	10/2019
9237	(2^200879+4730)/2	60471	Stefano Morozzi	10/2019
9238	(2^200875+118430)/2	60470	Stefano Morozzi	10/2019
9239	(2^200875+160250)/2	60470	Stefano Morozzi	10/2019
9240	(2^200874+153430)/2	60469	Stefano Morozzi	10/2019
9241	(2^200874+29482)/2	60469	Stefano Morozzi	10/2019
9245	12869^14714-14714^12869	60468	Norbert Schneider	04/2019
9242	(2^200869+185354)/2	60468	Stefano Morozzi	10/2019
9243	(2^200871+108038)/2	60468	Stefano Morozzi	10/2019
9244	(2^200871+127998)/2	60468	Stefano Morozzi	10/2019
9246	(2^200868+112786)/2	60467	Stefano Morozzi	10/2019
9247	(2^200866+35790)/2	60467	Stefano Morozzi	10/2019
9248	(2^200863+91010)/2	60466	Stefano Morozzi	10/2019
9249	(2^200860+66082)/2	60465	Stefano Morozzi	10/2019
9250	(2^200859+8150)/2	60465	Stefano Morozzi	10/2019

Find by discoverer :

PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)